## Fourier decay for limit sets

## Friends Talk with Sabine Schmidtke

## On the mathematical theory of black holes I

On the reality of black holes. I will give a quick introduction to the initial value problem in GR and overview of the problems of Rigidity, Stability and Collapse and how they fit with regard to the Final State Conjecture.

## Numerical Simulations of Black Hole Accretion

## On the mathematical theory of black holes II

I will discuss in some detail the main difficulties of the problem of nonlinear stability of black holes and the recent advances on the related issue of linear stability.

## Transfer operators for (relative) functoriality "beyond endoscopy" II

"Beyond endoscopy", broadly interpreted, is the idea that functoriality should be realized as a comparison between stable trace formulas. The nature of this comparison, however, remains completely unclear.

## On the mathematical theory of black holes III

I will discuss a recent result in collaboration with J. Szeftel concerning the nonlinear stability of the Schwarzschild spacetime under axially symmetric, polarized perturbations.